The newton (symbol: N) is the unit of
force
In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
in the
International System of Units (SI). Expressed in terms of
SI base units
The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
, it is 1 kg⋅m/s
2, the force that accelerates a mass of one kilogram at one metre per second squared.
The unit is named after
Isaac Newton
Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
in recognition of his work on
classical mechanics
Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
, specifically
his second law of motion.
Definition
A newton is defined as 1 kg⋅m/s
2 (it is a named derived unit defined in terms of the
SI base unit
The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...
s).
One newton is, therefore, the force needed to
accelerate one
kilogram
The kilogram (also spelled kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram" is formed from the combination of the metric prefix kilo- (m ...
of mass at the rate of one
metre per second squared
The metre per second squared or metre per square second is the unit of acceleration in the International System of Units (SI). As a derived unit, it is composed from the SI base units of length, the metre, and of time, the second. Its symbol i ...
in the direction of the applied force.
The units "metre per second squared" can be understood as measuring a rate of change in
velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...
per unit of time, i.e. an increase in velocity by one metre per second every second.
In 1946, the
General Conference on Weights and Measures (CGPM) Resolution 2 standardized the unit of force in the
MKS system of units
The metre, kilogram, second system of units, also known more briefly as MKS units or the MKS system, is a physical system of measurement based on the metre, kilogram, and second (MKS) as base units. Distances are described in terms of metres, mass ...
to be the amount needed to accelerate one kilogram of mass at the rate of one metre per second squared. In 1948, the 9th CGPM Resolution 7 adopted the name ''newton'' for this force.
The MKS system then became the blueprint for today's SI system of units.
The newton thus became the standard unit of force in the (SI), or
International System of Units
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
.
The connection to Newton comes from
Newton's second law of motion
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:
# A body re ...
, which states that the force exerted on an object is directly proportional to the acceleration hence acquired by that object, thus:
where
represents the
mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
of the object undergoing an acceleration
. When using the SI unit of mass, the kilogram (kg), and SI units for distance
metre
The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
(m), and time,
second
The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...
(s) we arrive at the SI definition of the newton: 1 kg⋅m/s
2.
Examples
At average
gravity on Earth (conventionally,
= ), a kilogram mass exerts a force of about 9.81 N.
* An average-sized
apple
An apple is a round, edible fruit produced by an apple tree (''Malus'' spp.). Fruit trees of the orchard or domestic apple (''Malus domestica''), the most widely grown in the genus, are agriculture, cultivated worldwide. The tree originated ...
with mass 200 g exerts about two newtons of force at Earth's surface, which we measure as the apple's
weight
In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition.
Some sta ...
on Earth.
:
* An
average adult exerts a force of about 608 N on Earth.
:
(where 62 kg is the world average adult mass).
Kilonewtons

Large forces may be expressed in kilonewtons (kN), where . For example, the
tractive effort of
a Class Y steam train locomotive and the
thrust
Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...
of an
F100 jet engine are both around 130 kN.
Climbing ropes are tested by assuming a human can withstand a fall that creates 12 kN of force. The ropes must not break when tested against 5 such falls.
[Bright, Casandra Marie. "A History of Rock Climbing Gear Technology and Standards." (2014).]
Conversion factors
See also
*
Force gauge
*
International System of Units
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
(SI)
*
Joule
The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...
, SI unit of
energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
, 1 newton exerted over a displacement of 1 metre
*
Kilogram-force
The kilogram-force (kgf or kgF), or kilopond (kp, from ), is a non-standard Gravitational metric system, gravitational metric unit of force. It is not accepted for use with the International System of Units (SI) and is deprecated for most uses. T ...
, force exerted by Earth's gravity at sea level on one kilogram of mass
*
Kip (unit)
*
Pascal, SI unit of
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
, 1 newton acting on an area of 1
square metre
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter ( American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square ...
*
Orders of magnitude (force)
*
Pound (force)
The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a Units of measurement, unit of force used in some System of measurement, systems of measurement, including English Engineering units and the foot–pound–second system.
Pou ...
*
Sthène
*
Newton metre
Newton most commonly refers to:
* Isaac Newton (1642–1726/1727), English scientist
* Newton (unit), SI unit of force named after Isaac Newton
Newton may also refer to:
People
* Newton (surname), including a list of people with the surname
* N ...
, SI unit of
torque
In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
References
{{Isaac Newton
Units of force
SI derived units
Isaac Newton